Durango Bill's
Bingo Probabilities
Bingo Probability Statistics Analysis
Data for Picture Frame (All 4 edges) and the Letter "Y"
The 2nd column in the table below shows the single-board probability that all four edges will be filled when the "Nth" number is called. The 3rd column shows the cumulative single-board probability that all four edges will be filled on or before the "Nth" number is called.
The 4th and 5th columns in the table show similar data, but for a large "Y" (Upper left to center, upper right to center, center to middle cell on the bottom row)
If we look at the table below we see that when the 20th number is called in a Bingo game, we get the following probabilities.
1) A single board has a 4.53331E-13 probability of filling all 4 edges when the 20th number is called.
2) A single board has a 5.66664E-13 probability of filling all 4 edges on or before 20 numbers are called.
3) A single board has a 5.77474E-05 probability of completing a "Y" when the 20th number is called.
4) A single board has a 0.000192491 probability of completing a "Y" on or before the 20th number is called.
Computer program and data by
Bill Butler
Quantity All 4 Edges Cumulative Letter Y Cumulative
of Bingo Probability Probability Probability Probability
Numbers This Turn All 4 Edges This Turn Letter Y
Picked 1 Board 1 Board 1 Board 1 Board
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1 0 0 0 0
2 0 0 0 0
3 0 0 0 0
4 0 0 0 0
5 0 0 0 0
6 0 0 4.96624E-09 4.96624E-09
7 0 0 2.97974E-08 3.47637E-08
8 0 0 1.04291E-07 1.39055E-07
9 0 0 2.78109E-07 4.17164E-07
10 0 0 6.25746E-07 1.04291E-06
11 0 0 1.25149E-06 2.2944E-06
12 0 0 2.2944E-06 4.58881E-06
13 0 0 3.93326E-06 8.52207E-06
14 0 0 6.39155E-06 1.49136E-05
15 0 0 9.94241E-06 2.4856E-05
16 1.16958E-16 1.16958E-16 1.49136E-05 3.97697E-05
17 1.87133E-15 1.98829E-15 2.16925E-05 6.14622E-05
18 1.59063E-14 1.78946E-14 3.07311E-05 9.21933E-05
19 9.54381E-14 1.13333E-13 4.25508E-05 0.000134744
20 4.53331E-13 5.66664E-13 5.77474E-05 0.000192491
21 1.81332E-12 2.37999E-12 7.69966E-05 0.000269488
22 6.34663E-12 8.72662E-12 0.000101058 0.000370546
23 1.99466E-11 2.86732E-11 0.000130781 0.000501327
24 5.73463E-11 8.60195E-11 0.000167109 0.000668436
25 1.52924E-10 2.38943E-10 0.000211085 0.000879521
26 3.82309E-10 6.21252E-10 0.000263856 0.00114338
27 9.03639E-10 1.52489E-09 0.000326679 0.00147006
28 2.03319E-09 3.55808E-09 0.000400925 0.00187098
29 4.37918E-09 7.93726E-09 0.000488082 0.00235906
30 9.07115E-09 1.70084E-08 0.000589766 0.00294883
31 1.81423E-08 3.51507E-08 0.000707719 0.00365655
32 3.51507E-08 7.03014E-08 0.000843819 0.00450037
33 6.6166E-08 1.36467E-07 0.00100008 0.00550045
34 1.21304E-07 2.57772E-07 0.00117867 0.00667912
35 2.17071E-07 4.74843E-07 0.00138189 0.008061
36 3.79874E-07 8.54717E-07 0.0016122 0.0096732
37 6.51213E-07 1.50593E-06 0.00187223 0.0115454
38 1.09522E-06 2.60115E-06 0.00216477 0.0137102
39 1.8095E-06 4.41065E-06 0.00249276 0.016203
40 2.94043E-06 7.35108E-06 0.00285935 0.0190623
41 4.70469E-06 1.20558E-05 0.00326783 0.0223301
42 7.41894E-06 1.94747E-05 0.00372169 0.0260518
43 1.15406E-05 3.10153E-05 0.00422462 0.0302765
44 1.7723E-05 4.87383E-05 0.00478049 0.035057
45 2.68901E-05 7.56284E-05 0.00539338 0.0404503
46 4.03351E-05 0.000115964 0.00606755 0.0465179
47 5.98522E-05 0.000175816 0.00680749 0.0533254
48 8.79079E-05 0.000263724 0.00761791 0.0609433
49 0.000127866 0.00039159 0.00850371 0.069447
50 0.000184277 0.000575867 0.00947005 0.078917
51 0.000263253 0.00083912 0.0105223 0.0894393
52 0.000372942 0.00121206 0.011666 0.101105
53 0.000524135 0.0017362 0.0129071 0.114012
54 0.000731031 0.00246723 0.0142515 0.128264
55 0.0010122 0.00347943 0.0157058 0.14397
56 0.00139177 0.0048712 0.0172764 0.161246
57 0.00190095 0.00677215 0.0189701 0.180216
58 0.00257987 0.00935202 0.0207942 0.20101
59 0.00347982 0.0128318 0.0227559 0.223766
60 0.00466612 0.017498 0.0248629 0.248629
61 0.0062215 0.0237195 0.0271232 0.275752
62 0.00825025 0.0319697 0.0295449 0.305297
63 0.0108833 0.042853 0.0321366 0.337434
64 0.0142843 0.0571373 0.0349069 0.372341
65 0.0186571 0.0757944 0.0378652 0.410206
66 0.0242542 0.100049 0.0410206 0.451227
67 0.0313878 0.131436 0.0443829 0.495609
68 0.040442 0.171878 0.0479622 0.543572
69 0.0518878 0.223766 0.0517687 0.59534
70 0.0663011 0.290067 0.0558132 0.651154
71 0.0843832 0.374451 0.0601065 0.71126
72 0.106986 0.481437 0.06466 0.77592
73 0.13514 0.616577 0.0694854 0.845405
74 0.17009 0.786667 0.0745946 0.92
75 0.213333 1 0.08 1
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